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Published on: June 8, 2018
Complexity of quantum states in the two-dimensional pairing model
J R Armstrong1, S Aberg, S M Reimann
1Winona State University, 175 W. Mark St, PA 120, Winona, MN 55987, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
Quantum chaos signatures emerge in interacting fermion systems with increasing pairing strength. However, dominant pairing forces lead to a regression towards regularity, revealing complex quantum state dynamics.
Area of Science:
- Quantum physics
- Many-body systems
- Quantum chaos
Background:
- Many-fermion systems like atoms and nuclei exhibit quantum chaos signatures at certain excitation energies.
- These signatures often align with predictions from random matrix theory.
- Understanding the emergence and evolution of quantum chaos is crucial for nuclear and atomic physics.
Purpose of the Study:
- To investigate the gradual development of quantum chaos signatures in a model many-fermion system.
- To analyze the influence of pairing interactions on the onset and regression of chaos.
- To differentiate between collective and chaotic complexity in quantum states.
Main Methods:
- Simulation of a model system with up to 16 fermions in a 2D harmonic trap.
- Study of interactions via short-range pairing forces.
- Analysis of level spacing distribution, eigenstate complexity, strength, and correlation functions.
- Introduction of a novel 'phase correlator' for state complexity analysis.
Main Results:
- Chaotic signatures gradually appear as pairing strength increases.
- A dominant pairing force leads to a regression towards regularity.
- The 'phase correlator' effectively distinguishes collective complexity from quantum chaotic complexity.
Conclusions:
- The development of quantum chaos in interacting fermion systems is sensitive to the strength of pairing interactions.
- A transition from chaos to regularity is observed under strong pairing conditions.
- The 'phase correlator' provides a new tool to interpret the nature of quantum state complexity.
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